May  2007, 7(3): 573-580. doi: 10.3934/dcdsb.2007.7.573

On shock waves in solids

1. 

Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, United States

Received  August 2006 Revised  January 2007 Published  February 2007

This paper describes some recent theoretical results pertaining to the experimentally-observed relation between the speed of a shock wave in a solid and the particle velocity immediately behind the shock. The new feature in the present analysis is the assumption that compressive strains are limited by a materially-determined critical value, and that the internal energy density characterizing the material is unbounded as this critical strain is approached. It is shown that, with this assumption in force, the theoretical relation between shock speed and particle velocity is consistent with many experimental observations in the sense that it is asymptotically linear for strong shocks of the kind often arising in the laboratory.
Citation: James K. Knowles. On shock waves in solids. Discrete & Continuous Dynamical Systems - B, 2007, 7 (3) : 573-580. doi: 10.3934/dcdsb.2007.7.573
[1]

Xiao-Biao Lin, Stephen Schecter. Traveling waves and shock waves. Discrete & Continuous Dynamical Systems - A, 2004, 10 (4) : i-ii. doi: 10.3934/dcds.2004.10.4i

[2]

Angelo Morro. Nonlinear waves in thermoelastic dielectrics. Evolution Equations & Control Theory, 2019, 8 (1) : 149-162. doi: 10.3934/eect.2019009

[3]

Paolo Paoletti. Acceleration waves in complex materials. Discrete & Continuous Dynamical Systems - B, 2012, 17 (2) : 637-659. doi: 10.3934/dcdsb.2012.17.637

[4]

Claude Vallée, Camelia Lerintiu, Danielle Fortuné, Kossi Atchonouglo, Jamal Chaoufi. Modelling of implicit standard materials. Application to linear coaxial non-associated constitutive laws. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1641-1649. doi: 10.3934/dcdss.2013.6.1641

[5]

Yuri Gaididei, Anders Rønne Rasmussen, Peter Leth Christiansen, Mads Peter Sørensen. Oscillating nonlinear acoustic shock waves. Evolution Equations & Control Theory, 2016, 5 (3) : 367-381. doi: 10.3934/eect.2016009

[6]

Mircea Bîrsan, Holm Altenbach. On the Cosserat model for thin rods made of thermoelastic materials with voids. Discrete & Continuous Dynamical Systems - S, 2013, 6 (6) : 1473-1485. doi: 10.3934/dcdss.2013.6.1473

[7]

Frederike Kissling, Christian Rohde. The computation of nonclassical shock waves with a heterogeneous multiscale method. Networks & Heterogeneous Media, 2010, 5 (3) : 661-674. doi: 10.3934/nhm.2010.5.661

[8]

Peter Howard, K. Zumbrun. The Evans function and stability criteria for degenerate viscous shock waves. Discrete & Continuous Dynamical Systems - A, 2004, 10 (4) : 837-855. doi: 10.3934/dcds.2004.10.837

[9]

Denis Serre, Alexis F. Vasseur. The relative entropy method for the stability of intermediate shock waves; the rich case. Discrete & Continuous Dynamical Systems - A, 2016, 36 (8) : 4569-4577. doi: 10.3934/dcds.2016.36.4569

[10]

Hualin Zheng. Stability of a superposition of shock waves with contact discontinuities for the Jin-Xin relaxation system. Kinetic & Related Models, 2015, 8 (3) : 559-585. doi: 10.3934/krm.2015.8.559

[11]

Eric Falcon. Laboratory experiments on wave turbulence. Discrete & Continuous Dynamical Systems - B, 2010, 13 (4) : 819-840. doi: 10.3934/dcdsb.2010.13.819

[12]

Edward Della Torre, Lawrence H. Bennett. Analysis and simulations of magnetic materials. Conference Publications, 2005, 2005 (Special) : 854-861. doi: 10.3934/proc.2005.2005.854

[13]

Joseph D. Fehribach. Using numerical experiments to discover theorems in differential equations. Discrete & Continuous Dynamical Systems - B, 2003, 3 (4) : 495-504. doi: 10.3934/dcdsb.2003.3.495

[14]

Michael Shearer, Nicholas Giffen. Shock formation and breaking in granular avalanches. Discrete & Continuous Dynamical Systems - A, 2010, 27 (2) : 693-714. doi: 10.3934/dcds.2010.27.693

[15]

Cristóbal Rodero, J. Alberto Conejero, Ignacio García-Fernández. Shock wave formation in compliant arteries. Evolution Equations & Control Theory, 2019, 8 (1) : 221-230. doi: 10.3934/eect.2019012

[16]

Maria Grazia Naso. Controllability to trajectories for semilinear thermoelastic plates. Conference Publications, 2005, 2005 (Special) : 672-681. doi: 10.3934/proc.2005.2005.672

[17]

Moncef Aouadi, Taoufik Moulahi. The controllability of a thermoelastic plate problem revisited. Evolution Equations & Control Theory, 2018, 7 (1) : 1-31. doi: 10.3934/eect.2018001

[18]

Moncef Aouadi, Taoufik Moulahi. Asymptotic analysis of a nonsimple thermoelastic rod. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1475-1492. doi: 10.3934/dcdss.2016059

[19]

Ramón Quintanilla, Reinhard Racke. Stability for thermoelastic plates with two temperatures. Discrete & Continuous Dynamical Systems - A, 2017, 37 (12) : 6333-6352. doi: 10.3934/dcds.2017274

[20]

John Murrough Golden. Constructing free energies for materials with memory. Evolution Equations & Control Theory, 2014, 3 (3) : 447-483. doi: 10.3934/eect.2014.3.447

2018 Impact Factor: 1.008

Metrics

  • PDF downloads (9)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]